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# Terrence has 2/3 as many cards as Phillip. If Terrence were to win one

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Math Expert
Joined: 02 Sep 2009
Posts: 58381
Terrence has 2/3 as many cards as Phillip. If Terrence were to win one  [#permalink]

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19 Feb 2019, 23:24
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:37) correct 40% (02:07) wrong based on 47 sessions

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Terrence has 2/3 as many cards as Phillip. If Terrence were to win one card from Phillip, he would have 3/4 as many cards as Phillip. If Terrence wins an even number of cards from Phillip, which of the following could be the number of cards that Phillip has left?

I. 19
II. 18
III. 17

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

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Joined: 18 Aug 2017
Posts: 5008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Terrence has 2/3 as many cards as Phillip. If Terrence were to win one  [#permalink]

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20 Feb 2019, 01:12
1
Bunuel wrote:
Terrence has 2/3 as many cards as Phillip. If Terrence were to win one card from Phillip, he would have 3/4 as many cards as Phillip. If Terrence wins an even number of cards from Phillip, which of the following could be the number of cards that Phillip has left?

I. 19
II. 18
III. 17

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

in best case scenario
Philip can have 21 cards in total ;
which sufficies all given relation
so if even cards are taken out ; Philip will have 19 cards or 17 cards left
IMO E
as odd-even = odd integer options would be correct..
Intern
Joined: 18 Jan 2019
Posts: 28
Re: Terrence has 2/3 as many cards as Phillip. If Terrence were to win one  [#permalink]

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22 Feb 2019, 01:03
Archit3110 wrote:
Bunuel wrote:
Terrence has 2/3 as many cards as Phillip. If Terrence were to win one card from Phillip, he would have 3/4 as many cards as Phillip. If Terrence wins an even number of cards from Phillip, which of the following could be the number of cards that Phillip has left?

I. 19
II. 18
III. 17

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

in best case scenario
Philip can have 21 cards in total ;
which sufficies all given relation
so if even cards are taken out ; Philip will have 19 cards or 17 cards left
IMO E
as odd-even = odd integer options would be correct..

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Terrence has 2/3 as many cards as Phillip. If Terrence were to win one  [#permalink]

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22 Feb 2019, 01:10
Ish1996 wrote:
Archit3110 wrote:
Bunuel wrote:
Terrence has 2/3 as many cards as Phillip. If Terrence were to win one card from Phillip, he would have 3/4 as many cards as Phillip. If Terrence wins an even number of cards from Phillip, which of the following could be the number of cards that Phillip has left?

I. 19
II. 18
III. 17

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

in best case scenario
Philip can have 21 cards in total ;
which sufficies all given relation
so if even cards are taken out ; Philip will have 19 cards or 17 cards left
IMO E
as odd-even = odd integer options would be correct..

Ish1996
Well I actually solved the question using answer options as hint..
so seeing 19,18,17 ; the best pick of the cards which Philip can have is 21
case 1: Terrence has 2/3 as many cards as Phillip; Terrence has ; 14 cards
now question says "If Terrence were to win one card from Phillip, he would have 3/4 as many cards as Phillip"
so
since P= 21 ; taking 1 card would make it 20 ; and adding 1 to T will make him have 15 cards ; or say T = 20*3/4 = 15

secondly : "If Terrence wins an even number of cards from Phillip, which of the following could be the number of cards that Phillip has left"

knowing the rule that odd integer-even integer ; odd integer ; we can say from given option that Philips would end with an odd integer count of cards upon giving even cards..
so option 19,17 are correct...

hope this helps..
Intern
Joined: 01 Jul 2018
Posts: 20
Re: Terrence has 2/3 as many cards as Phillip. If Terrence were to win one  [#permalink]

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15 Apr 2019, 13:47
Statement tells us:
>Philip has x cards
>Terrence has 2x/3 cards

ratio:

P/T = x / (2x/3)

hint from statement:

P-1/T+1 = x / 3x/4

(substitute P and T by our initial values)--> x-1/(2x/3 + 1) = x/(3x/4) ---> if we solve for x, we get: x=21

so Philip has 21 cards initially, which means that Terrence has 2/3*(21)=14 cards.

(now play with the answer options) --> if we remove an even number from poor Philip, e.g. 2, he's left with 21-2=19 (answer choice I). Also, removing 4, he'd be left with 21-4=17 (answer choice III).
Thus, IMO E
Re: Terrence has 2/3 as many cards as Phillip. If Terrence were to win one   [#permalink] 15 Apr 2019, 13:47
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